流体力学+第三讲

calmon
4 ℃
2020-05-17

整理文档很辛苦，赏杯茶钱您下走！

还剩 ... 页未读，继续阅读 >>

免费阅读已结束，点击下载阅读编辑剩下 ... 页

阅读已结束，您可以下载文档离线阅读编辑

资源描述

2:12451219H~Pn~VdS=Rr(P~V)dV;~Pn=~nPx1.10ox1x2x3ox01x02x03ijij=cos(~e0i;~ej)=~e0i~ejox1x2x3;~ej;j=1;2;3ox01x02x03;~e0i;i=1;2;3~e0i=ij~ej;~ei=ji~e0jO~ej~e0iij~e0iij~e0i=ij~ej=cos(~e0i;~e1)~e1+cos(~e0i;~e2)~e2+cos(~e0i;~e3)~e3(1)~ei~e0j~ei=ji~e0j;~ej=kj~e0k(2)(2)(1)(ki+ijkj)~e0k=0)ijkj=ik;jijk=ik~e0i~ej;j=1;2;3()ij=~e0i~ej=cos'ji=~e0j~ei~e0i=ij~ej=i1~e1+i2~e2+i3~e3~e0i~e0k=ij~ejkm~em=ijkmjm=ijkj=ik~ei~ek=ji~e0jmk~e0m=jimkjm=jijk=ikijik=jk;jiki=jk1'(x01;x02;x03;t)='(x1;x2;x3;t)a0i=ijaja1;a2;a3~aox1x2x3~a=ai~eiox01x02x03~a=a0j~e0j2~a=ai~ei=aiji~e0j)a0j=jiai0BBBBBBBBBBB@1112132122233132331CCCCCCCCCCCAai=jia0jjiNnox1x2x332PmnP0ij=imjnPmn32PmnP=Pmn=0BBBBBBBBBBB@P11P12P13P21P22P23P31P32P331CCCCCCCCCCCAnox1x2x33nPj1j2jnox01x02x033nP0i1i2in=i1j1i2j2injnPj1j2jn23nnn01P0=P131P0i=ijPj232P0ij=ikjmPkm333P0ij`=ikjm`nPkmn:::::::::n3nP0j1j2jn=j1k1j2k2jnknPk1k2knijijij=0ij*ikjk=ij)0ij=ikj`k`ij21P=Pj1j2jnQ=Qj1j2jnnPQTT=Tj1j2jn=Pj1j2jnQj1j2jnnPQP=QPQP=QPQ=0P0Q0=00)P0=Q0PQ2P=Pi1i2immQ=Qj1j2jnnTi1i2imj1j2jn=Pi1i2imQj1j2jn3Tm+nT=PQP''Qn~a~baibj~a~b=aibjnPP=Pj1j2jn~ej1~ej2~ejn3P=Pj1j2jnn2Qn2P0i1i2in2kk=i1j1i2j2in2jn2krksPj1j2jn2rs=i1j1i2j2in2jn2rsPj1j2jn2rs=i1j1i2j2in2jn2Pj1j2jn2rrQ=Pi1i2in2kkn2P4PQmPnQm+n2PQPQP~a=Pijaj~aP=aiPijP~a,~aPP;QPQ=PikQkjP;QP:Q=PijQjix**P=Pi1i2imj1j2jnnQ=Qj1j2:::jnPi1i2imj1j2jnQj1j2:::jnmPm+nmTP0i1i2imj1j2jnQ0j1j2:::jn=T0i1i2im=i1k1i2k2imkmTk1k2km=3i1k1i2k2imkmPk1k2kmr1r2rnQr1r2rn=Pk1k2kmr1r2rni1k1i2k2imkmj1r1j2r2jnrnQ0j1j2jn(P0i1i2imj1j2jni1k1i2k2imkmj1r1j2r2jnrnPk1k2kmr1r2rn)Q0j1j2:::jn=0Q0nP0i1i2imj1j2jn=i1k1i2k2imkmj1r1j2r2jnrnPk1k2kmr1r2rn4Pm+nPi1i2imnQPi1i2imQj1j2jn=Ti1i2imj1j2jnm+nPi1i2immx1.111.P=PijPc=PjiPPij=PjiPPij=PjiP2.P=A+SA=12(PPc)S=12(P+Pc)!1;!2;!3A=aij=0BBBBBBBBBBB@0a12a31a120a23a31a2301CCCCCCCCCCCA=0BBBBBBBBBBB@0!3!2!30!1!2!101CCCCCCCCCCCAaij=ijk!k1.Aa0ij=imjkamka0ji=jkimakm=imjkamk=a0ij2.!1;!2;!3~!3.A~bA~b=~!~b~bA=~b~!A~!=(!1;!2;!3)A~b=aijbj=ijkbj!k=~!~bx1.1251.nP=Pi1i2inrPrP=gradP=@@xkPi1i2inpi1i2inkn+1r0P0=@@x0kP0i1i2in=@x`@x0k(i1k1i2k2inkn@@x`Pk1k2kn)=i1k1i2k2inknk`@@x`Pk1k2kn2.nP=Pi1i2inrPrP=divP=@@xkPki2inrPn1~adiv~a=r~a=@ai@xi~ar~a=@ai@xj3.IS~nPdS=ZVdivPdV(1)ISnkPkj2jndS=ZV@@xkPkj2jndV(1)1P'r('P)='rP+r'Pr('P)=@@xk('Pkj)=@'@xkPkj+'@Pkj@xk='rP+r'P2div(~a~b)=~b(r~a)+(~ar)~bdiv(~a~b)=@@xk(akbj)=@ak@xkbj+ak@bj@xk=~b(r~a)+(~ar)~b3r(~ar~a)=r~a:r~a+~ar(r~a)r(~ar~a)=@@xjai@aj@xi!=ai@2aj@xj@xi+@ai@xj@aj@xi=r~a:r~a+~ar(r~a)6